Download Worksheet-ProblemsFromA16.2

Problems from A16.2 Vector Fields:
E
F
q
g
F
m
E
Ve
r
g
(Assume all these fields are uniform)
Vg
r
1. A gravitational field increases the potential of a mass from 35.0 J/kg at point A to 89.0 J/kg at point B in a
vertical distance of 2.50 m. What is the field strength, and what force does it exert on a 23.0 kg mass? Does
the field point toward B or A? (21.6 N/kg, 497 N, toward A)
2. An electric field exerts a Southerly force of 1.30 N on a +780. µC charge. What is the change in potential if
you displace yourself 5.30 m to the north? (+8830 V)
3. A gravitational field exerts a force of 140. N on a 17.0 kg mass away from point B and toward point A that is
vertically displaced from B a distance of 45.0 m. What is the field strength? What is the change in
gravitational potential if you go from B to A? (8.24 N/kg, -371 J/kg)
4. An upward electric field has a strength of 23,400 N/C. What is the change in potential if you displace
yourself upward 3.40 cm? What force will it exert on an electron? A proton?
(-796 J/C or V, 3.75x10-15 N down, 3.75x10-15 N up)
5. If you move 12.0 m West in an electrical field, your electrical potential drops by 340. V. What is this
electrical field? What force does this field exert on a charge of -56.0 µC? (28.3 V/m (or N/C) to the West, 1.59x10-3 N East)
6. A gravitational field has a strength of 1.10x10-7 N/kg to the right. If I move a mass 2.30 m to the left, what is
the change in gravitational potential? What force does this exert on a 1.00 gram object? (+2.53x10-7 J/kg, 1.10x10-10 N)
7. An electrical field changes electrical potential from 210. V to 560. V when you move down 4.50 cm. What is
the magnitude and direction of the electrical field, and what force does it exert on a +2.40 µC charge?
(7780 V/m (or N/C) up, 0.0187 N up)
8. An electrical field exerts a force of 78.0 N to the left on a -12.0 µC charge. What is the magnitude and
direction of this electrical field? What is the change in electrical potential if you move 13.0 cm to the left?
(6.50x106 N/C right, +8.45x105 V)
9. The leftmost of two vertical parallel plates is held at -12.0 V, and the rightmost is held at +16.0 V. If they are
separated by 3.20 cm, what is the electrical field between them? What force would it exert on an electron
between the plates? (875 V/m to the left, 1.40x10-16 N to the right)
10. If you move a mass vertically from point A to point Bin a uniform gravitational field, the potential changes
from -45.0 J/kg to -12.0 J/kg in a distance of 3.40 m. What is the gravitational field strength, and which point
is at a higher elevation, A or B? Does the field point toward A or B? What force does it exert on a 2.30 kg
mass (g = 9.71 N/kg toward A, B is higher, 22.3 N)
g
GM
r2
E
kq
r2
( not in data packet - memorize this!!!!)
11. The electric field is 52.0 N/C downwards 54.0 cm above a charge. What is the charge, and is it positive or
negative? (-1.69x10-9 C, negative)
12. What is the electric field 230. m above a +21.0 µC charge? What direction is it? (3.57 N/C up)
13. Near a -18.0 C charge there is an upward electric field of 450. N/C. How far away is the point where this
happens, and where is it, above or below the charge? (19.0 m, below)
14. There is an electric field of 310. N/C upwards 88.0 cm above an unknown charge. What is the charge, and is
it positive or negative? (2.67x10-8 C, positive)
15. What is the electric field 2.70 m to the left of a +8.20 C charge? What direction is it? (1.01x104 N/C, left)
16. At what distance from the center of a 6.90x1024 kg planet is the gravitational field 4.50 N/kg? (1.01x107 m)
17. What is the acceleration of gravity on the surface of a planet with a mass of 6.39x1023 kg and a radius of
3.39x106 m? (Mars) (3.71 N/kg)
18. What is the gravitational field 4.50 m to the right of a 2.80x1012 kg point mass? What direction? (9.22 N/kg left)
19. Near a 3.40x1012 kg point mass there is a field of 5.60 N/kg to the left. What distance are we from the point
mass, and where is the mass in relation to us? (6.36 m, the mass is to our left)
20. There is a gravitational field of 14.0 N/kg to the right, 7.20 m from a point mass. What is the mass, and
where are we in relation to the mass? (1.09x1013 kg, we are to the left of the mass)
21.
A. Find the gravitational field at p and q:
6
4.30x10 m
m
(p: 8.29 N/kg left, q: 8.23 N/kg left)
6.20x106 m
(p)
4.80x106 m
m
(q)
24
3.50x1024 kg
2.50x10 kg
B. Find the gravitational field at p and q: (p: 10.7 N/kg right, q: 28.3 N/kg left)
6.30x106 m
m
5.60x106 m
(p)
4.90x106 m
m
(q)
24
5.90x1024 kg
9.70x10 kg
C. Find the electrical field at p and q: (p: 2.37 N/C left, q: 452 N/C left)
(p)
18.0 m
+
-
32.0 m
13.0 m
(q)
-8.60 µC
+1.20 µC
D. Find the electrical field at p and q: (p: 54.9 N/C right, q: 2.01 N/C right)
(p)
26.0 m
-
21.0 m
(q)
-3.50 µC
24.0 m
-4.70 µC
22. Each grid line is a meter. Calculate the field at point p.
A. Charge A is +1.30 µC, B is +3.10 µC
B. Mass A is 9.40x1012 kg, mass B is 1.80x1012 kg
2698 N/C up and right at 31.6o with the x axis
38.8 N/kg down and right (barely) at 85.0o with the x axis
C. Charge A is -6.50 µC, B is -4.10 µC
D. Mass A is 1.40x1012 kg, mass B is 1.20x1012 kg
3850 N/C, up and left at 61.8o with the x axis
14.4 N/kg to the right and up at 54.9o with the x axis
E. Charge A is -3.70 µC, B is +5.30 µC
F. Mass A is 2.90x1012 kg, mass B is 8.70x1012 kg
4970 N/C right and up (barely) at 1.26o with the x axis
49.8 N/kg left and down at 62.8o with the x axis